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Khách
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2 tháng 10 2016
a) \(xy+y^2-x-y=y\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(y-1\right)\)
b) \(25-x^2+4xy-4y^2=25-\left(x-2y\right)^2=\left(5-x+2y\right)\left(5+x-2y\right)\)
c) \(x^2-4x+3=x^2-x-3x+3=x\left(x-1\right)-3\left(x-1\right)=\left(x-1\right)\left(x-3\right)\)
d) \(y^2\left(x-1\right)-7y^3+7xy^3\)
\(=y^2\left(x-1-7y+7xy\right)\)
\(=y^2\left[\left(x-1\right)-7y\left(1-x\right)\right]=y^2\left(x-1\right)\left(1+7y\right)\)
2 tháng 10 2016
a)
\(xy+y^2-x-y\\ =\left(xy-x\right)+\left(y^2-y\right)\\ =x\left(y-1\right)+y\left(y-1\right)\\ =\left(y-1\right)\left(x+y\right)\)
LP
1
MT
25 tháng 8 2015
a) 9x^2+6xy+y^2
=(3x+y)2
b)6x - 9 - x^2
=-(x2-6x+9)
=-(x-3)2
c) x^2 + 4y^2 + 4xy
=(x+2y)2
NH
2
10 tháng 7 2019
\(A=\left(6x-3y\right)+\left(4x^2-4xy+y^2\right)\)
\(=3\left(2x-y\right)+\left(2x-y\right)^2\)
\(=\left(3+2x-y\right)\left(2x-y\right)\)
\(B=9x^2-\left(y^2-4y+4\right)\)
\(=9x^2-\left(y-2\right)^2\)
\(=\left(3x+y-2\right)\left(3x-y+2\right)\)
NN
10 tháng 7 2019
A = ( 6x - 3y ) + (4x2 - 4xy + y2 )
A = 3.( 2x - y) + [ ( 2x )2 - 2.2.x.y + y2 ]
A = 3.( 2x - y ) + ( 2x - y )2
A = ( 2x - y ).(3 + 2x - y )
B = 9x2 - ( y2 - 4y + 4 )
B = ( 3x )2 - ( y - 2 )2
B = ( 3x - y + 2 ).( 3x + y - 2 )
C = - 25x2 + y2 - 6y + 9
C = ( y2 - 2.3.y + 32 ) - ( 5x )2
C = ( y - 3 )2 - ( 5x )2
C = (y - 3 - 5x ).( y - 3 +5x )
D = x2 - 4x - y2 -- 8y - 12
D = ( x2 - 4x + 4 ) - 4 - y2 - 8y -12
D = ( x - 2.2x + 22 ) - ( y2 + 2.4.y + 42 )
D = ( x - 2 )2 - ( y + 4 )2
D = ( x - 2 + y + 4 ).( x - 2 - y - 4 )
D = ( x + y + 2 ).( x - y - 6 )
NH
1
24 tháng 8 2019
\(48-4y^2-4y=-\left(4y^2+4y-48\right)\)
\(=-\left[\left(2y\right)^2+2.2y+1-49\right]\)
\(=-\left[\left(2y+1\right)^2-7^2\right]\)
\(=-\left(2y-6\right)\left(2y+8\right)\)
NH
1
21 tháng 8 2019
\(48-4y^2-4y\)
\(=-\left(4y^2+4y-48\right)\)
\(=-\left(4y^2+4y+1-49\right)\)
\(=-\left[\left(2y+1\right)^2-7^2\right]\)
\(=-\left(2y+1-7\right)\left(2y+1+7\right)\)
\(=-\left(2y-6\right)\left(2y+8\right)\)
\(=-4\left(y-3\right)\left(y+4\right)\)
14 tháng 10 2020
a) \(9\left(2x-3\right)^2-4\left(x+1\right)^2\)
\(=\left[3\left(2x-3\right)-2\left(x+1\right)\right]\left[3\left(2x-3\right)+2\left(x+1\right)\right]\)
\(=\left(6x-9-2x-2\right)\left(6x-9+2x+2\right)\)
\(=\left(4x-11\right)\left(8x-7\right)\)
b) \(\left(x^2+4y^2-20\right)-16\left(xy-4\right)^2\)
\(=\left[\left(x^2-4xy+4y^2\right)-4\right]\left[\left(x^2+4xy+4y^2\right)-36\right]\)
\(=\left[\left(x-2y\right)^2-4\right]\left[\left(x+2y\right)^2-36\right]\)
\(=\left(x-2y-2\right)\left(x-2y+2\right)\left(x+2y-6\right)\left(x+2y+6\right)\)
KN
14 tháng 10 2020
a. 9 ( 2x - 3 )2 - 4 ( x + 1 )2
= [ 3 ( 2x - 3 ) ]2 - [ 2 ( x + 1 ) ]2
= [ 3 ( 2x - 3 ) - 2 ( x + 1 ) ] [ 3 ( 2x - 3 ) + 2 ( x + 1 ) ]
= ( 6x - 9 - 2x - 2 ) ( 6x - 9 + 2x + 2 )
= ( 4x - 11 ) ( 8x - 7 )
b. ( x2 + 4y2 - 20 )2 - 16 ( xy - 4 )2
= ( x2 + 4y2 - 20 )2 - [ 4 ( xy - 4 ) ]2
= [ x2 + 4y2 - 20 - 4 ( xy - 4 ) ] [ x2 + 4y2 - 20 + 4 ( xy - 4 ) ]
= ( x2 + 4y2 - 20 - 4xy + 16 ) ( x2 + 4y2 - 20 + 4xy - 16 )
= ( x2 + 4y2 - 4xy - 4 ) ( x2 + 4y2 + 4xy - 36 )
= [ ( x - 2y )2 - 22 ] [ ( x + 2y )2 - 62 ]
= ( x - 2y - 2 ) ( x - 2y + 2 ) ( x + 2y - 6 ) ( x + 2y + 6 )
(1)\(\left(3x\right)^2+2×3x+y^2=\left(3x+y\right)^2\)
(2)\(-x^2+6x-9=-\left(x^2-6x+9\right)=-\left(x^2-6x+3^2\right)=-\left[\left(x-3\right)^2\right]\)
(3)\(x^2+4xy+4y^2=x^2+2×x×2y^2+\left(2y\right)^2=\left(x+2y\right)^2\)